Bayesian adaptive tensor ring decomposition with automatic model selection

Area of Science:

• Machine Learning
• Computer Vision
• Data Science

Background:

• Robust tensor decomposition (RTD) is crucial for analyzing noisy high-dimensional data in machine learning and computer vision.
• Existing RTD methods struggle with automatic noise adaptation and determining appropriate model complexity.
• Challenges include handling unknown noise distributions and selecting optimal tensor ranks.

Purpose of the Study:

• Introduce a robust non-parametric Bayesian method, Bayesian adaptive tensor ring decomposition (BATR).
• Address limitations of current RTD methods in automatic noise adaptation and model capacity determination.
• Develop a method for enhanced tensor decomposition in machine learning and computer vision applications.

Main Methods:

• Utilize a Dirichlet process Gaussian mixture model (DP-GMM) to model unknown noise and automatically determine noise components.
• Incorporate a generalized hyperbolic (GH) prior for adaptive low tensor ring (TR) rank modeling, enabling automatic TR rank determination.
• Employ a variational Bayesian inference algorithm for efficient posterior updates.

Main Results:

• BATR demonstrates superior performance compared to state-of-the-art methods.
• Experiments show effectiveness across diverse datasets including synthetic data, color images, face images, multispectral, and hyperspectral images.
• The method successfully handles noise adaptation and model capacity determination.

Conclusions:

• BATR offers a robust and adaptive solution for tensor decomposition challenges.
• The proposed Bayesian approach provides automatic noise and rank determination, improving performance in machine learning and computer vision.
• BATR represents a significant advancement in handling noisy high-dimensional data.